Integral approximations to classical diffusion and smoothed particle hydrodynamics
Integral approximations to classical diffusion and smoothed particle hydrodynamics
复制标题
经典扩散和平滑粒子流体动力学的积分近似
DOI：
10.1016/j.cma.2014.12.019
复制
发表时间：
2015
影响因子：
7.2
通讯作者：
A. Tartakovsky
中科院分区：
文献类型：
--
作者：
Q. Du;R. Lehoucq;A. Tartakovsky
本文的贡献是用一个带体积约束的积分方程解一个经典扩散算子。一个特别的焦点是与Neumann边界条件相关的经典扩散问题。通过利用这个近似值，我们还可以近似其他量，例如出域的通量。我们在连续介质水平上对模型方程的分析与最近关于非局域扩散和动力学力学的工作密切相关。特别是，我们阐明了在存在物理边界的情况下，体积约束作为经典Neumann边界条件的近似所起的作用。然后，体积约束积分方程为精确和稳健的离散化方法提供了基础。一个直接的应用是理解和改进光滑粒子流体动力学(SPH)方法。
The contribution of the paper is the approximation of a classical diffusion operator by an integral equation with a volume constraint. A particular focus is on classical diffusion problems associated with Neumann boundary conditions. By exploiting this approximation, we can also approximate other quantities such as the flux out of a domain. Our analysis of the model equation on the continuum level is closely related to the recent work on nonlocal diffusion and peridynamic mechanics. In particular, we elucidate the role of a volumetric constraint as an approximation to a classical Neumann boundary condition in the presence of physical boundary. The volume-constrained integral equation then provides the basis for accurate and robust discretization methods. An immediate application is to the understanding and improvement of the Smoothed Particle Hydrodynamics (SPH) method.
影响因子：
1
作者：
Li X;Lowengrub J;Rätz A;Voigt A
通讯作者：
Voigt A